Evaluating perturbation contributions in SAFT models by comparing to molecular simulation of n-alkanes

SAFT models are generally written as a perturbation series of the Helmholtz energy with reciprocal temperature as the argument. The perturbation coefficients are then functions of density and molecular size. The variation of the perturbation coefficients with molecular size is given primarily by Wertheim's theory [6-9], but there may be additional variations as in the PC-SAFT model. In the present work, we compare the characterization of perturbation coefficients inferred from PC-SAFT to those derived from molecular simulations.The molecular simulations are based on Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic Perturbation Theory (TPT). DMD simulation is applied to the repulsive part of the potential model with molecular details like fused hard spheres for the interaction sites and 110° bond angles. The thermodynamic effects of disperse attractions are treated by rigorous application of TPT. The present work re-examines the related work of Elliott and Gray [35] in the low density and critical regions, focusing on n-alkanes with carbon numbers ranging from 3 to 80.We find that SAFT theory overestimates the repulsive contribution (A₀) and underestimates the first order contribution (A₁) of Helmholtz energy relative to simulation. Nevertheless, the correlations are qualitatively reasonable. Significant inconsistencies arise when considering the second order contribution (A₂). For example, the PC-SAFT characterization of A₂ becomes larger than A₁ in the low density, long chain limit, raising concerns about the convergence of the series. Furthermore, fluctuations are underestimated in the critical region and overestimated in the liquid region. In each case, we can suggest improved characterizations. Altogether, these results suggest ways to modify the SAFT formalism to achieve greater consistency between atomistic and coarse-grained models.